Abstract
In the stage of modelling, measuring, mechanical processing and manufacturing of the nonlinear energy harvesting system, deviations and errors of system parameters are inevitable. Even slight variation of key parameters may have a significant influence on the output voltages, especially for the multi-stable nonlinear case. Therefore, the investigation of dynamic behaviors for the tristable energy harvesting system with uncertain parameters is of important value both for research and application. In this paper, the uncertainty of a tristable piezoelectric vibration energy harvester with a random coefficient ahead of the nonlinear term is studied. By using the Chebyshev polynomial approximation, this tristable energy harvesting system is first reduced into an equivalent deterministic form, the ensemble mean responses of which are derived to exhibit the stochastic behaviors. The periodic and chaotic motions, bifurcations and crises under different conditions are analyzed. The results show that the output voltage is sensitive to the uncertainty of the nonlinear coefficient, which leads to unstable behavior around the bifurcation and crisis points particularly. Exploring the influence pattern of uncertain parameters on the output voltage and avoiding the unstable parameter intervals are essential for optimizing the structure. It can further improve the efficiency of the nonlinear energy harvesting system.
Highlights
With the rapid development of wireless sensor networks and portable electronics, conventional batteries have not held pace with the demands from microelectronic devices
We find that the stochastic dynamics phenomenon of the tristable energy harvester (TEH) can be affected more by the bigger intensity of uncertain parameter
The ensemble mean response of this deterministic system can be obtained, and the validity of this method is verified by the numerical simulation
Summary
With the rapid development of wireless sensor networks and portable electronics, conventional batteries have not held pace with the demands from microelectronic devices. The simulated results illustrated that small variations of key design parameters can lead to a significant impact on the output electrical power Taking it one step further, a reliability analysis of the vibration energy harvesting device under physical uncertainty was proposed [32], with the aim of calculating the probability of overall system success. The sensitivity of the harvested power to variations in the harvester’s parameters was assessed for optimal design [33], which showed that the harvested power is most sensitive to variations of eccentricity These above-mentioned studies illustrated that the uncertainty of the system parameter may lead to obvious changes of system dynamic responses and reliability, so the parametric uncertainty analysis of an energy harvesting system needs to be further discussed.
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